Charlie is older than Ava. Their ages are consecutive even integers. Find Charlie's age if the product of their ages is 80

Answer:

c=10

Step-by-step explanation:

pythagreom theroem

c (hypotenuse) = \(\sqrt{a^{2} +b^{2} }\)

plug in values for a and b

c=\(\sqrt{6^{2} +8^{2} }\)

c=\(\sqrt{36+64\\}\)

c=\(\sqrt{100\\}\)

c=10

Answer:

length of the hypotenuse = √100 = 10 ft

Step-by-step explanation:

This is a right triangle with leg lengths 6 and 8 ft.  We apply the Pythagorean Theorem a^2 + b^2 = c^2, as follows:

(6 ft)^2 + (8 ft)^2  = c^2

Then c^2 = 100, and c = length of the hypotenuse = √100 = 10 ft

The width of the pool is 22 meters, and the length is 25 meters.

The area of Rectangle is length times of width.

Let w be the width of the pool.

The pool is 3 meters longer than its width which is length

L=w+3

The walk around the pool is 2 meters wide,

The total width of the pool and walk is w + 4 and the total length is w + 3 + 4 = w + 7.

The total area of the pool and walk is "268 square meters more than the area of the pool

(w + 4)(w + 7) = w(w) + 268.

Now we can simplify and solve for "w":

w² + 11w + 28 = w^2 + 268

11w = 240

w = 22

Hence, the width of the pool is 22 meters, and the length is 3 meters longer, which is 25 meters.

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Answer:

36 back

Step-by-step explanation:

100 - 64 = 36

Answer:

36¢

Step-by-step explanation:

1.00-0.64=0.36

Answer:

6:6=3:3=1:1=160/2=80

160/2=80 male

160/2=80 female

80 female

In order to determine the maximum revenue, consider that the revenue is equal to the product of the price and the quantity of products sold.

Based on the information of the question, you have:

Revenue = price * quantity

R(x) = (30 + x)(4000 - 100x)

where R is the function for the revenue.

Use distribution property to expand the previous factor:

(30 + x)(4000 - 100x) = 30(4000) + 30(-100x) + x(4000) + x(-100x)

= 120000 - 3000x + 4000x - 100x²

= 120000 + 1000x - 100x²

to determine the maximum, calculate the derivative of the previous expression, equal to zero and solve for x, as follow:

R'(x) = 1000 - 200x = 0

-200x = -1000

x = 1000/200

x = 5

next, replace the previous value of x into the formula for R(x):

R(5) = (30 + 5)(4000 - 100(5))

R(5) = (35)(3500)

R(5) = 122500

Hence, the maximum total revenue possible is $122,500

Answer:

Radius is 12 (24/2)

Diameter is 24 (a straight line passing from side to side through the center of a circle)

The root of the equation sinx = 2x-3 is 0.8401 (approx).

Given equation is sinx = 2x-3

We need to solve this equation using false position method.

False position method is also known as the regula falsi method.

It is an iterative method used to solve nonlinear equations.

The method is based on the intermediate value theorem.

False position method is a modified version of the bisection method.

The following steps are followed to solve the given equation using the false position method:

1. We will take the end points of the interval a and b in such a way that f(a) and f(b) have opposite signs.

Here, f(x) = sinx - 2x + 3.

2. Calculate the value of c using the following formula: c = [(a*f(b)) - (b*f(a))] / (f(b) - f(a))

3. Evaluate the function at point c and find the sign of f(c).

4. If f(c) is positive, then the root lies between a and c. So, we replace b with c. If f(c) is negative, then the root lies between c and b. So, we replace a with c.

5. Repeat the steps 2 to 4 until we obtain the required accuracy.

Let's solve the given equation using the false position method.

We will take a = 0 and b = 1 because f(0) = 3 and f(1) = -0.1585 have opposite signs.

So, the root lies between 0 and 1.

The calculation is shown in the attached image below.

Therefore, the root of the equation sinx = 2x-3 is 0.8401 (approx).

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Je vais décrire les étapes pour tracer les figures demandées à main levée et indiquer les informations pertinentes sur chaque figure. Cependant, je ne suis pas en mesure de les tracer en "vraie grandeur" ici, car je ne peux fournir que des représentations textuelles. Voici les étapes pour les deux figures :

1) Figure IFGH :

2) Figure RSTU de centre O :

Assurez-vous de tracer les segments et les angles avec soin et de les proportionner selon les dimensions indiquées.\(\)

Step-by-step explanation:

second one is right

I hope

Answer:

Step-by-step explanation:

Let equal sides of an isosceles triangle = a inches

Base = \(\frac{1}{2}a+2\) inches

Perimeter  = 32 inches

a + a + \(\frac{1}{2}a+2\) = 32

\(2a + \frac{1}{2}a+2 = 32\\\\\frac{2a*2}{1*2}+\frac{1}{2}a+2=32\\\\\frac{4a}{2}+\frac{1}{2}a+2=32\\\\\frac{5}{2}a+2 = 32\\\\\)

Subtract 2 from both sides

\(\frac{5}{2}a=32-2\\\\\frac{5}{2}a=30\\\\a=30*\frac{2}{5}\\\\a=6*2\)

a = 12 inches

base = \(\frac{1}{2}*12+2\)

        = 6 + 2

Base = 8 inches

To find a linear differential operator that annihilates the function 1 + 8e^(2x), we can start by differentiating the function.

d/dx (1 + 8e^(2x)) = 0 + 16e^(2x) = 16e^(2x)

Notice that the derivative of the function is a constant multiple of itself. This suggests that the linear differential operator we are looking for involves a constant coefficient multiplied by the derivative operator.

Let's try multiplying the derivative operator d/dx by a constant c and applying it to the function:

c(d/dx)(1 + 8e^(2x)) = c(0 + 16e^(2x)) = 16ce^(2x)

We want this result to be equal to zero, so we can solve for the constant c:

16ce^(2x) = 0

c = 0

Therefore, the linear differential operator that annihilates the function 1 + 8e^(2x) is simply d/dx. In other words, taking the derivative of the function will result in zero.

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\(-7x-9y=-8\)

\(5x+6y=4\)

\(-35x-45y=-40\)

\(35x+42y=28\)

\(-3y=-12\)

\(y=4\)

\(5x+6(4)=4\)

\(5x+24=4\)

\(5x=-20\)

\(x=-4\)

\((-4,4)\)

Hope this helps.

頑張って!

Answer:

Below

Step-by-step explanation:

The avg. weight of a cat is around 8 pounds

The avg. of a large dog is around 130 pounds.

Since they give no other numbers to go off of, I would just plug these in.

The dog would be 122 pounds heavier than the dog.

I’m sorry if this isn’t what you’re looking for, I think I need more information.

Answer: \(x=-7\)

Step-by-step explanation:

\(4x-5 =-33\)

ad 5 to both sides

\(4x=-28\)

divide both sides by 4

\(x=-7\)

plug in x to double check

\(4(-7)-5=-33\\-28-5=-33\\-33=-33\)

hope this helps :3

The correct answer is b. 80%. This can be answered  by the concept of correlation coefficient.

The correlation coefficient (r) is a measure of the strength and direction of the linear relationship between two variables. It can range from -1 to 1, where -1 indicates a perfect negative correlation, 0 indicates no correlation, and 1 indicates a perfect positive correlation.

In this case, a correlation coefficient of 0.8 indicates a strong positive correlation between the two variables. This means that 80% of the variation in the response variable can be explained by the variation in the explanatory variable.

To calculate the percentage of variation explained by the explanatory variable, we square the correlation coefficient (r²) and multiply by 100. In this case, (0.8)² = 0.64, and 0.64 x 100 = 64%.

However, the question is asking for the percentage of variation explained by the explanatory variable, not the correlation coefficient itself, so the correct answer is 80%.

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Answer:

x= 75*2

x= 3/4*200

(The options arent very clear)

Step-by-step explanation:

The equation is

x= 75/100 *200

= 75*2

or 3/4 * 200

Answer:

The answer is B.

Step-by-step explanation:

Step-by-step explanation:

1/11 + 1/2

2/22 + 11/22= 13/22

Answer:

B. (5x+7)

Step-by-step explanation:

i did same question on a quiz yesterday lol

The value of Kb will be  1.83 × 10⁻¹¹.

The given problem states that Ka is equal to 5.47×10⁻⁴, and the task is to find Kb. Ka and Kb are related to each other through the equation Kw = Ka × Kb. Kw represents the ion product of water, which is equal to the concentration of H₃O⁺ ions multiplied by the concentration of OH⁻ ions. It has a value of 1.0 × 10⁻¹⁴.

Using the fact that pKw = pH + pOH = 14.00, we can determine the relationship between pKa and pKb. By rearranging the equation, we get pKa + pKb = 14.00. This equation relates the logarithms of the acid dissociation constant (pKa) and the base dissociation constant (pKb).

To find Kb, we can use the formula Kb = Kw/Ka. Substituting the given values, we have Kb = (1.0 × 10⁻¹⁴)/(5.47 × 10⁻⁴). Simplifying this expression, we find Kb = 1.83 × 10⁻¹¹.

Therefore, the value of Kb is determined to be 1.83 × 10⁻¹¹.

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Answer:

60 or 6

Step-by-step explanation:

which one

Answer:

(-8.5, 7).

Step-by-step explanation:

the two points are (-10, 3) and (-7, 11). Let's plug in the values into the midpoint formula:

M = ((-10 + -7) / 2, (3 + 11) / 2)

Simplifying the calculations:

M = (-17 / 2, 14 / 2)

M = (-8.5, 7)

i hope i helped you!

The exponent of the expression is 6.

Remember that a superscript is a small symbol on the right top of another, then we can write this as:

7⁶

Remember that a general power is:

aⁿ

Where a is the base and n is the exponent.

Comparing that with the given expression, we can see that the base is 7 and the exponent is 6.

So the first option is the correct one.

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To prove that f is one-to-one function, it must be proven that f(x1)=f(x2) and x1=x2.

What is a one to one function?

The mapping of two sets is essentially what a one to one function refers to. When every element in a function's range and domain match exactly one another, the function is said to be one-to-one.

The one-to-one function, also known as an injective function, is one of the many different types of functions.

A function that transfers different components of its domain to different elements of its codomain is known as a one-to-one function.

For example, a function  f:A→B  is said to be one-to-one if -

f(x1)=f(x2)⇒x1=x2

for all elements x1,x2∈A.

To prove  f:A→B  is one-to-one -

Consider the fact that f(x1)=f(x2).  

Then it must be true that x1=x2.

Therefore, it is now understood that f is one-to-one by definition if f(x1)=f(x2) and x1=x2.

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Answer:

140 ft²

Step-by-step explanation:

First, we divide the figure into the two visible polygons. The first being a right angled triangle and the second being a rectangle.

Area of a right angled triangle = 0·5 × b × h

= 0·5 × 6 × 4 I've included a picture to show where the 6 and 4 came from

= 12 ft²

Area of a rectangle = l × w

= 16 × 8

= 128 ft²

Add the two areas to get the area of the figure

= 128 + 12

∴ the area of the figure is 140 ft²

The intervals are nested, each subsequent interval is contained within the previous one. Mathematically, this means I₁ ⊇ I₂ ⊇ ... In ⊇ ... . Therefore, we have:

1. I₁ ⊇ I₂ implies [a₁; b₁] ⊇ [a₂; b₂], which means a₁ ≤ a₂ and b₁ ≥ b₂.
2. I₂ ⊇ I₃ implies [a₂; b₂] ⊇ [a₃; b₃], which means a₂ ≤ a₃ and b₂ ≥ b₃.

To show that a1 ≤ a2 ≤ ... ≤ an ≤ ..., we need to use the fact that the sequence of intervals is nested, meaning that each interval is contained within the next one.

First, we know that I1 contains I2, so every point in I2 is also in I1. That means that a1 ≤ a2 and b1 ≥ b2.

Now consider I2 and I3. Again, every point in I3 is also in I2, so a2 ≤ a3 and b2 ≥ b3.

We can continue this process for all the intervals in the sequence, until we reach In. So we have:

a1 ≤ a2 ≤ ... ≤ an-1 ≤ an

and

b1 ≥ b2 ≥ ... ≥ bn-1 ≥ bn

This shows that the endpoints of the intervals are ordered in the same way.

Given that I₁ ⊇ I₂ ⊇ ... In ⊇ ... is a nested sequence of intervals and In = [an; bn], we can show that a₁ ≤ a₂ ≤ ... ≤ an ≤ ... and b₁ ≥ b₂ ≥ ... ≥ bn ≥ ... as follows:

Since the intervals are nested, each subsequent interval is contained within the previous one. Mathematically, this means I₁ ⊇ I₂ ⊇ ... In ⊇ ... . Therefore, we have:

1. I₁ ⊇ I₂ implies [a₁; b₁] ⊇ [a₂; b₂], which means a₁ ≤ a₂ and b₁ ≥ b₂.
2. I₂ ⊇ I₃ implies [a₂; b₂] ⊇ [a₃; b₃], which means a₂ ≤ a₃ and b₂ ≥ b₃.

Continuing this pattern for all intervals in the sequence, we can conclude that a₁ ≤ a₂ ≤ ... ≤ an ≤ ... and b₁ ≥ b₂ ≥ ... ≥ bn ≥ ... .

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To make a table of values for a linear relationship;

Choose a group of x values before creating the table. Add each x value from the left side column to the equation. Evaluate the equation (middle column) to arrive at the y value

Given,

Linear relationship;

A straight-line link between two variables is referred to statistically as a linear relationship (or linear association). Linear relationships can be represented graphically or mathematically as the equation y = mx + b.

Here,

We have to make a table of values for a linear relationship;

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Answer: 12

Step-by-step explanation:

Answer:

its the middle one

Step-by-step explanation:

had this on a test, got it right

Answer:

Step-by-step explanation:

delete this if you want bc im not answeing i just wanted to say there nothing there

Answer:

There are many answers in my opinion but I think the answer is 60 multiple choice questions I feel like I'm wrong I probably am but that's my answer

Step-by-step explanation:

Answer:

(2x*+6)(x-2)

2x(x-2)+6(x-2)

2xx+2x(-2)+6x +6(-2)

we know ;

(-). (-) = +

(-). (+) = -

(+). (-) = -

(+). (+) = +

2xx-2x(2)+6x -6(2)

2x^2  - 4x + 6x  -12

2x^2  - 2x  -12

Step-by-step explanation: